Rewrite as a simplified fraction. ${1.5\overline{1} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 151.1111...\\ 10x &= 15.1111...\end{align*}}$ Subtracting the two equations, we have: ${90x = 136}$ ${x = \dfrac{136}{90}} $ ${x = \dfrac{68}{45}} \text{or} {1 \dfrac{23}{45}}$